@Sffcorgi They do look like parrots though? White is a clearly a Cockatoo, Black/Red looks a lot like a Black-winged Lorie, and Brown could possibly be counted as a Greater Vasa Parrot (though they are usually black there are some brown ones)

I finally got a Rare Parrot just after I was beginning to believe they didn't really exist! I've been hunting this one for many weeks in the Swamp, Un'Goro, and Stranglethorn but found it in Swamp of Sorrows directly across from Stonard near the mountains (the Shifting Mire where the Lost Ones are). Coordinates were 46.72, 33.99 and it was the primary pet.

Bloodsail Admiral am I, and adventured across open sea and land along side my trusty parrot have I. But alas my hat he is much too fond of and of it no longer am I. The smell of my adventuring and of things worse hangs heavy about it. So I tasked myself to find another such companion to accompany me while I in my cleaner wear, even if be he only poor. I found such a rare friend, and his rare cockroach friend, and as thanks for his friendhship I have sacrificed his friend.

Zenhunter does not seem to be wrong with regards to finding this pet in Stranglethorn. I did not find one in North Stranglethorn but I found two in The Cape of Stranglethorn, both as another pet that had joined the battle.

Caught mine in a fight while looking for a rare Strand Crab in Stranglethorn. Tamed an uncommon because i didn't have one yet, and haven't looked back since! By far the best pet i have for fighting snakes, and regluarly masters snakes several levels higher.

Mine summons in mostly white (the color when captured),some browns and a yellow. Just now, he came to a battle dressed in the Blue/red. Yeay! I'm wondering if the frequency of skin color is tied randomly to the pet, the region caught, or just a set factor.